A Mixed Integer Linear Programming Formulation for Unrestricted Wind Farm Layout Optimization

Discrete complex-valued code pathfinder algorithm for wind farm layout optimization problem

Optimal operation of water-energy microgrids; a mixed integer linear programming formulation

One of the main obstacles in using mixed integer linear programming (MILP) formulations for large-scale open pit production scheduling is the size of the problem. The objective of this work is to develop, implement, and verify deterministic MILP formulations for long-term large-scale open pit production scheduling problems. The objective of the model is to maximize the net present value, while meeting grade blending, mining and processing capacities, and the precedence of block extraction constraints. We present four MILP formulations; the first two models are modifications of available models; we also propose, test and validate two new MILP formulations. To reduce the number of binary integer variables in the formulation, we aggregate blocks into larger units referred to as mining-cuts. We compare the performances of the proposed models based on net present value generated, practical mining production constraints, size of the mathematical programming formulations, the number of integer variables required in formulation, and the computational time required for convergence. An iron ore mine case study is represented to illustrate the practicality of the models as well.

Unrestricted wind farm layout optimization (UWFLO): Investigating key factors influencing the maximum power generation

The visual impact of wind farm layouts has seen little consideration in the literature on the wind farm layout optimisation problem to date. Most existing algorithms focus on optimising layouts for power or cost of energy alone. In this paper, we consider the geometry of wind farm layouts and whether it is possible to bi-optimise a layout for both energy efficiency and the degree of visual impact that the layout exhibits. We develop a novel optimisation approach for solving the problem, with our approach towards measuring mathematically the degree of visual impact drawing inspiration from the field of architecture. To evaluate our ideas, we demonstrate them on three benchmark problems for the wind farm layout optimisation problem in conjunction with two recently published stochastic local search algorithms. Optimal patterned layouts are shown to be very close in terms of energy efficiency to optimal non-patterned layouts.

The BlockCopy stochastic local search algorithm is a state-of-the-art optimiser for the Wind Farm Layout Optimisation problem. Unlike many other metaheuristics-based optimisers, BlockCopy requires the specification of only one key parameter, namely a block size. In this paper, we investigate the effect on different block sizes on the optimisation results. Using standard benchmarks for the Wind Farm Layout Optimisation problem, we show that smaller fixed block sizes (relative to overall layout size) produce better optimised layouts than larger fixed block sizes. More interestingly, we also show that randomising the block size parameter results in optimisation performance at the same or a better level than that produced by the best algorithm with a fixed block size. Effectively, this means that the user can ignore the need to tune the block size parameter and simply randomise it instead. Such a strategy results in what is effectively a parameterless, but none-the-less effective, optimisation algorithm for the Wind Farm Layout Optimisation problem.

Layout optimization of a wind farm considering grids of various resolutions, wake effect, and realistic wind speed and wind direction data: A techno-economic assessment

The creation of wakes, with unique turbulence characteristics, downstream of turbines significantly increases the complexity of the boundary layer flow within a wind farm. In conventional wind farm design, analytical wake models are generally used to compute the wake-induced power losses, with different wake models yielding significantly different estimates. In this context, the wake behavior, and subsequently the farm power generation, can be expressed as functions of a series of key factors. A quantitative understanding of the relative impact of each of these factors is paramount to the development of more reliable power generation models; such an understanding is however missing in the current state of the art in wind farm design. In this paper, we quantitatively explore how the farm power generation, estimated using four different analytical wake models, is influenced by the following key factors: (i) incoming wind speed, (ii) land configuration, and (iii) ambient turbulence. The sensitivity of the maximum farm output potential to the input factors, when using different wake models, is also analyzed. The extended Fourier Amplitude Sensitivity Test (eFAST) method is used to perform the sensitivity analysis. The power generation model and the optimization strategy is adopted from the Unrestricted Wind Farm Layout Optimization (UWFLO) framework. In the case of an array-like turbine arrangement, both the first-order and the total-order sensitivity analysis indices of the power output with respect to the incoming wind speed were found to reach a value of 99%, irrespective of the choice of wake models. However, in the case of maximum power output, significant variation (around 30%) in the indices was observed across different wake models, especially when the incoming wind speed is close to the rated speed of the turbines.

The optimal scheduling of crude-oil operation in refineries has been studied by various groups during the past decade leading to different mixed integer linear programming or mixed nonlinear programming formulations. This paper presents a new formulation with oil residency time constraint based on single-operation sequencing (SOS). It is different from previous formulations as it considers oil residency time constraint and pipeline transfer and does not require to postulate the number of priority-slots in which operations take place. This model is also based on the representation of a crude-oil scheduling by a single sequence of transfer operations. A simple MILP procedure has been used to solve this model leading to an satisfactory optimal result.

Optimal design of wind farm layout using a biogeographical based optimization algorithm

A multi-objective bi-level location problem for heterogeneous sensor networks with hub-spoke topology

Combined heating and cooling networks with part-load efficiency curves: Optimization based on energy hub concept

Strong cutting planes for the capacitated multi-pickup and delivery problem with time windows

Mobile Edge Computing (MEC) is a new paradigm which has been introduced to solve the inefficiencies of mobile cloud computing technologies. The key idea behind MEC is to enhance the capabilities of mobile devices by forwarding the computation of applications to the edge of the network instead of to a cloud data-center. One of the main challenges in MEC is determining an efficient placement of the components of a mobile application on the edge servers that minimizes the cost incurred when running the application. In this paper, we address the problem of multi-component application placement in edge computing by designing an efficient heuristic on-line algorithm that solves it. We also present a Mixed Integer Linear Programming formulation of the multi-component application placement problem that takes into account the dynamic nature of users' location and the network capabilities. We perform extensive experiments to evaluate the performance of the proposed algorithm. Experimental results indicate that the proposed algorithm has very small execution time and obtains near optimal solutions.

An interactive method for the selection of design criteria and the formulation of optimization problems in computer aided optimal design